Method and a device for measuring the three dimension surface shape by projecting moire interference fringe

ABSTRACT

A method and apparatus for measuring contour of a full fielded 3D surface of an object. The apparatus includes a projection device having a mark point and master grating, an imaging device for imaging imaged grating and mark point which are positioned on the object surface, and two rectilinearly movable axles. The method includes steps of: measuring a projected object and image distances, and an imaged object and image distances; determining a position of the zero order phase of the fringe according to an imaged mark point on the object surface; calculating orders of the moire fringes for the full fielded 3D surface of the object based on a phase-shift and unwrapping algorithms; and finally calculating an absolute contour of 3D object surface according to a relationship between altitudes of surface points of the object and the moire fringes referencing to a point of the object surface which is derived as a reference point of 3D coordinates.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is related to a method and apparatus for threedimensional (3D) surface measurement, and more particularly related to amethod and apparatus for analyzing absolute contour of full fielded 3Dsurface of objects applying a projected moire fringe interferometry.

2. Description of the Prior Art

Measuring contour of three dimensional surface of objects attractsattention in the society of engineering and technology. The currentlyavailable commercial apparatus for 3D surface measurement includes atype of instrument for measuring three-coordinate data of objects whichis relied on mechanically contacting each point of the object surface,and another type of laser instrument of measuring three-coordinate dataof objects. The instrument for the contacting measurement is equippedwith a mechanical probe. The probe which is driven by a numericalcontrol mechanism travels on the surface of an object under measurementto thereby provide the three-coordinate data for every point of theobject surface. Accuracy of the spatial measurement is generally betterthan 0.01 mm for the instrument. However, a measuring speed of theinstrument is relatively slow, since it takes times for the numericalsystem to move across the surface while the mechanical probe appliesforces at certain extent to the object.

In stead of applying the mechanical probe, the laser instrument employsan optical probe which is driven by a numerical control system. Anoptical spot generated by the optical probe scans surface of an object.In general, the laser instrument improves the measuring speed whilesuffering a loss of some degree of the accuracy in the spatialmeasurement. However, increase of the measuring speed for the laserinstrument is still limited by the moving speed of the numerical controlsystem. Therefore, a full field measurement of the object will beoptimum if it can largely increase the measuring speed.

A moire image including moire fringes is obtained from applying aprojected moire interferometry. The fringes are produced frominterfering an optical image of a master grating, when the image isoptically positioned on a submaster grating. The projected moireinterferometry is a full field non-contacting technique for measurementof characteristics of the object surface, which possesses a plurality ofmeasuring capabilities as compared with a holographic interferometry.However, it is more important that, the projected moire interferometryenables controlling its sensitivity in measurement so that the moireinterferometry is excellent to reject external interference. For thisreason, there is a great prospect of utilizing the projected moireinterferometry in engineering applications.

A moire contouring is a promising optical method for imaging objectsurface, which is originally introduced by Takasaki and Meadows et. al.An apparatus which applies the method is actually quite simple,including a grating which is positioned adjacent an object so thatshadow fringes can be observed on the object after projecting lightsthrough the grating. The shadow fringes are equivalent to lines of themoire contouring under certain conditions, which can be used to measuresurface characteristics of objects. The method is particularly useful tomeasure objects having small sizes since the grating size limitsapplication of the apparatus only to the small objects.

Another method of the moire contouring is respectively introduced byBenoit, P.; Yoshino, Y.; Suzuki, M. and others. The method includesprojecting an image of grooves of a master grating onto the surface ofan object to thereby image a graph of the moire contour of the objectthrough a submaster grating. The method is referred to the projectedmoire interferometry, which is particularly useful to measure objectshaving large sizes. Under certain conditions, beat fringes generatedfrom a combining effect of the master grating and submaster gratingprovide lines of a contour map of the imaged object surface, which isanalogous to the way a topographic map delineates the contour of theland. In the early 1980s, image processing was successfully introducedfor analyzing the moire fringes. Core technologies of the imageprocessing particularly include a phase shift algorithm and unwrappingalgorithm, which makes the projected moire fringe interferometry enableto perform a real-time measurement.

According to studies of Meadows, Takasak and Suzuki et. al, the moirefringes become the respective lines of the surface contour map for anobject if following criteria are met: optical centers of the respectiveprojection and imagining optical axe are in parallel; spaces of therespective projecting master grating and imaging submaster grating arethe same; focal lengths of the respective projection lens and imaginglens are the same; and distance between the projection grating and lensis the same as compared with distance between the imaging grating andlens.

Referring to FIG. 1, there is illustrated a prior art moireinterferometer, wherein a light source 1 projects light rays which passthrough a projection master grating 2, so that an image of grooves ofthe master grating is focused on an object 4 under measurement after thelights optically pass through a projection lens 3. An image of themeasured object is then positioned on a submaster grating 6 in additionto moire fringes which are also formed. Images of the formed moirefringes are then optically recorded by a camera 8 through a camera lens7.

However, there are two unresolved problems which have persistentlyassociated with the projected moire interferometry long time ago. Thefirst one is that contour lines of the contour map for the objectsurface, which are described by the moire fringes, are function oforders of the fringes. Therefore, differences in attitude are not equalfor respective two adjacent contour lines of the map. In fact, theattitude difference is also a function of the fringe order. Therefore,it is necessary to accurately determine the absolute orders of the moirefringes if absolute appearance of the 3D object surface is desired. Thesecond problem is a necessity of accurately measuring object distancesbetween the respective projection device to the object, and the imagingdevice to the object, and imaging distances between the respectiveprojection grating to the object, and the image grating to the object.The currently available projected moire interferometer is unable toaccurately measure the above mentioned distances. In stead, it is from arough measurement to estimate the object distances and image distances,according to an assumption that the attitude differences between therespective two adjacent contour lines are constant.

SUMMARY OF THE INVENTION

Purpose of the Invention

It is therefore an objective of the present invention to provide amethod and apparatus from an improved projected moire fringeinterferometry which overcomes the problems of the currently availabletechniques for measuring surface contour. The present invention methodand apparatus can measure the absolute contour of the object surfacewith high accuracies in combination with advantage of the real-timeanalysis from the prior projected moire interferometry.

Contents of the Invention

The techniques which are applied to realize the objective of the presentinvention include an apparatus for measuring contour of the 3D surfaceof objects. The apparatus is comprised of a projection device includinga mark point and master grating, an imaging device including a markpoint and submaster grating, and a first and second rectilinearlymovable axles aligning with the respective x and y axe of the x-ycoordinate system. Application of the rectilinearly movable coordinateaxles can construct a right angled triangle from using the mark point ofthe projection device, the mark point of the imaging device, and animage of the mark point of the projection device which is projected toan exterior surface of the object, wherein they are at an arbitrarypositions where an image of the object can be formed.

The first rectilinearly movable axle having a first grating ruler isaligned with an optical axis of the imaging device, which is positionedperpendicular to the second rectilinearly movable axle having a secondgrating ruler. In addition, an optical axis of the projection deviceintersects the second rectilinearly movable axle at an angle γ. Theoptical axe of the respective projection device and imaging deviceintersects each other at an angle θ, wherein the angles γ and θ arecomplementary.

The present invention of the measurement apparatus also includes animage capture board to digitize image signals and a computer to processthe digitized images.

The projection device from the present invention includes a lightsource, a master grating, a mark point, and a movable projection lens,wherein the mark point can be positioned behind the master grating, orin parallel with the master grating.

The imaging device from the present invention includes a light path formeasuring purpose, wherein optical components which are positionedwithin the light path include a camera, a submaster grating, a markpoint which can be switched in and off the light path, and a movableimaging lens, wherein the mark point is positioned in parallel with thesubmaster grating.

In addition, the imaging device form the present invention can also haveanother preferred embodiment including a light path for image inaddition to the light path for measurement. The light path formeasurement has optical components including a camera, submastergrating, and a movable imaging lens. The light path for image includes acamera which records an image of a mark point, a reflection mirror whichreflects an incident light at an angle of 90 degrees, the mark point,and a square prism which is positioned between the imaging lens and thesubmaster grating, wherein the prism can split an incident light to twoemerging lights, which one emerging light travels along a direction with90 degrees to another emerging light aligning with the incident light.

The disclosed master and submaster gratings of the respective projectionand imaging devices from the present invention can be a type of theRonchi grating or sinusoidal grating. The mark points have the shape ofa circle or cross.

The light which is employed in the present invention includes a whitelight.

The illustrated movable projection lens which is positioned inside ofthe projection device includes a linear positioner which can move thelens. Similarly, the illustrated movable imaging lens which ispositioned inside of the imaging device includes a linear positioner formoving the lens.

The present invention includes the method of measuring contour of the 3Dobject surface, wherein the method is comprised of the stops of:

(1) establishing a right angled triangle from connecting the mark pointof the projection device, the mark point of the imaging device, and theimage of the mark point of the projection device which is projected ontothe object surface;

(2) determining a conjugated projecting distance, and a conjugatedimaging distance;

(3) calculating a projected object and image distances, and imagedobject and image distances;

(4) focusing automatically of the respective projection lens and imaginglens in accordance with the calculated projected object and imagedistances, and the calculated imaged object and image distances to formthe moire fringes on the submaster grating of the imaging device;

(5) calculating a phase distribution through the object surface fromapplying the phase-shift algorithm and unwrapping algorithm in referenceof a zero order of the phase which is defined as the image of the markpoint which is projected on the object; and

(6) calculating a height distribution.

Accordingly, the present invention method includes: first establishingthe right angled triangle from applying the mark point of the projectiondevice, mark point of the imaging device, and the image of the markpoint of the projection device which is projected onto the objectsurface; measuring the respective projected object and image distances,and the respective imaged object and image distances at a position wherean image is formed, wherein the measurement is conducted from using themark points of the respective projection and imaging devices, and therectilinearly movable axles which are aligned with the respective x andy coordinate axe; then determining the position of a moire fringe havingthe zero-order phase according to the image of the mark point of theprojection device, which is projected on the surface of the object;deciding orders of the moire fringes positioned in a full field of theobject surface from applying the phase-shift algorithm and unwrappingalgorithm; and finally calculating an accurate contour of the object 3Dsurface according to relationships of altitudes of the object surfacepoints and the moire fringes in reference of a point of the objectsurface which serves as a reference point of the coordinates.

The right angled triangle as illustrated above is established throughthe following steps: moving the object into a viewable field of theimaging device; focusing an image of the mark point which is projectedon the object surface; and aligning the image of the mark point on theobject surface with the mark point of the imaging device.

The conjugated projection and imaging distances, which are illustratedabove, are determined from the following steps: calculating lengths ofthe respective two sides of a right angled triangle ΔADE from applying aknown length of the rest one side and a known degree of an angle of thetriangle, where AE=AD/tg θ; DE=AD/sin θ. The angle θ is between theoptical axe of the respective projection and imaging devices, which canbe calculated from: θ=arc tg R₂/R₁. AD is a distance between theprojection and imaging device, which is measured from a reading of thesecond grating ruler (a length of the second rectilinearly movable axlewhich forms one side of the right angled triangle ΔADE), R₁ and R₂ aremoved distances of the respective master and submaster gratings, AE isan imaged conjugated distance between the object and submaster gratingof the imaging device, and DE is a projected conjugated distance betweenthe master grating of the projection device and the object.

Therefore, the projected object and image distances, and the imagedobject and image distances can be calculated according the followingrespective equations:

${Z_{C} + Z_{CF}} = \frac{AD}{{tg}\;\vartheta}$${\frac{1}{Z_{C}} + \frac{1}{Z_{CF}}} = \frac{1}{F_{1}}$${L_{P} + L_{PF}} = \frac{AD}{\sin\;\vartheta}$${\frac{1}{L_{P}} + \frac{1}{L_{PF}}} = \frac{1}{F_{2}}$where, Z_(C) is the imaged object distance, Z_(CF) is the imaged imagedistance, L_(PF) is the projected image distance, L_(P) is the projectedobject distance, F₁ is the focal length of the imaging device, and F₂ isthe focal length of the projection device.

The present invention enables to construct the moire fringes which arepositioned on the submaster grating of the imaging device from the stepof automatically focusing. The operation of the automatically focusingmoves the projection lens and imaging lens to the respective positionsso that the moire fringes are formed, wherein the movement is conductedaccording to the calculated data including the projected object andimage distances, and the imaged object and image distances.

Finally, the present invention enables to calculate the heightdistribution according to the following equations:

$Z = {- \frac{{\left( {\frac{\varphi}{2\pi\; f} + X_{C}} \right)D} - {L_{PF}B}}{{\left( {\frac{\varphi}{2\;\pi\; f} + X_{C}} \right)C} - {L_{PF}A}}}$$X_{Z} = {\frac{Z + Z_{C}}{Z_{CF}}X_{C}}$$Y_{Z} = {\frac{Z + Z_{C}}{Z_{CF}}Y_{C}}$where X_(Z), Y_(Z), and Z are the respective coordinates for a point ofthe object surface which is spatially positioned, f is a gratingfrequency, and φ is a phase.A=Z _(C) Z _(CF) sin θ+Z _(C) X _(C) cos θ B=Z _(C) ² X _(C) cos θC=Z _(C) Z _(CF) cos θ−Z _(C) X _(C) sin θ D=−Z _(C) ² X _(C) sin θ+Z_(C) Z _(CF) L _(P)

The following is a detailed disclosure of the present inventionapparatus and method taken in conjunction with the drawings andexamples. However, referring particularly to the examples is for thepurpose of illustration only and not limitation of the presentinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

Referring particularly to the drawings for the purpose of illustrationonly and not limitation, there is illustrated:

FIG. 1 is a schematic diagram of main structural elements for a priorart of the moire interferometry;

FIG. 2 is a diagrammatic representation of the present inventionapparatus for measuring contour of a full field three dimensionalsurface of an object by applying the moire fringes;

FIG. 3 is a schematic diagram which illustrates optical components for apreferred embodiment of a projection device of the present inventionapparatus;

FIG. 4 is a schematic diagram which illustrates optical components for apreferred embodiment of an imaging device from the present inventionapparatus;

FIG. 5 is a schematic diagram, which illustrates relationship ofcalculated parameters from the present invention;

FIG. 6 is a schematic diagram to illustrate principles which are used inmeasurement of appearance of the object applying the moire fringes;

FIG. 7 is a flow chart which illustrates steps of the present inventionmethod for measuring contour of a full field three dimensional surfaceof an object by applying the moire fringes;

FIG. 8 is a schematic diagram which illustrates optical components fromanother embodiment of the projection device of the present inventionapparatus; and

FIG. 9 is a schematic diagram which illustrates optical components fromanother embodiment of the imaging device of the present inventionapparatus.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Although specific embodiments of the present invention will now bedescribed with reference to the drawings, it should be understood thatsuch embodiments are by way of example only and merely illustrative ofbut a small number of the many possible specific embodiments which canrepresent applications of the principles of the present invention.Various changes and modifications obvious to one skilled in the art towhich the present invention pertains are deemed to be within the spirit,scope and contemplation of the present invention as further defined inthe appended claims.

Referring to FIG. 2, there is illustrated structural components of thepresent invention apparatus for measuring contour of a full field threedimensional surface of an object by applying projected moire fringeinterferometry. The apparatus is comprised of an imaging device 20, afirst rectilinearly movable axle 40 and a first grating ruler 60 whichare positioned to align with an optical axis of the imaging device 20,and an object 80 positioned on a rotating objective receiving support 30which is rotatably affixed to a movable plate 41, wherein the movableplate 41 is slidably connected to the first rectilinearly movable axle40.

The apparatus further includes a second rectilinearly movable axle 50and a second grating ruler 70 which are positioned to perpendicular tothe first rectilinearly movable axle 40, a projection device 10 which ispositioned on the second rectilinearly movable axle 50 and whose opticalaxis intersects the axle 50 at an angle γ, and a marble platform 90which affixes including the first rectilinearly movable axle 40 and thefirst grating ruler 60, the second rectilinearly movable axle 50 and thesecond grating ruler 70, and the imaging device 20. In addition, thepresent invention apparatus additionally includes an image capture board100 which is used to digitize image signals, and a computer 110 forprocessing the digitized image signals.

As illustrated in FIG. 3, the projection device 10 is comprised ofoptical components including a light source 11 which is positioned infront of a condenser 12, a master grating 13 whose grooves arepositioned on one surface of the grating, a mark point 14 which ispositioned on the opposite surface of the grating, and a projection lens15. The master grating 13 is movable aligning with an orientation of thegrating surface, wherein the movement of the grating 13 is controlled bya linear positioner 17. Similarly, the projection lens 15 is movablealigning with an optical axis of the projection device, wherein themovement of the lens 15 is controlled by a linear positioner 16.

It will be appreciated that, as illustrated the projection device 10 inFIG. 8, the mark point 14 can be positioned in parallel with the groovesof the master grating 13.

The imaging device 20 is comprised of a measuring light path, whichincludes a camera 21, a switcher 27 for switching a mark point 25positioned and the submaster grating 23, and a movable imaging lens 29

Referring to FIG. 9, the measuring light path includes a camera 21having a camera lens 22 which records images of the moire fringespositioned on the submaster grating, the switcher 27 which can switchthe mark point 25 and the submaster grating 23 respectively in or offthe optical axis of the imaging device, and the movable imaging lens 29whose movement aligning with the optical axis is controlled by a linearpositioner 29A.

It will be appreciated that, as illustrated in FIG. 4, the imagingdevice 20 includes an alternative embodiment comprising a measuringlight path 120 and imaging light path 130. The imaging optical path 130includes the movable imaging lens 29, the linear positioner 29A whichcontrols the movement of the movable imaging lens 29 aligning with anoptical axis of the lens 29, a square prism 24 which is positionedbetween the image lens 29 and submaster grating 23 for splitting anincident light into a first and second emerging lights, wherein thefirst emerging light is aligned with the incident light and the secondemerging light is departing from the first emerging light at an angle of90 degrees, a mark point 25 which is positioned between the square prism24 and a reflection mirror 26, wherein the mirror 26 reflects the secondemerging light at an angle of 90 degrees, an imaging camera 28 having acamera lens 27 for recording the imaged mark point 25. The measuringoptical path 120 includes the movable image lens 29, the linearpositioner 29A which controls movement of the lens 29 along its opticalaxis, the measuring camera 21 having the camera lens 22 for receivingimages of the moire fringes positioned on the submaster grating 23.

Referring now to FIG. 7, there is illustrated a flow chart of thepresent invention method to measure contour of a full field 3D surfaceof an object. During the measurement, first move the measured object 80along the first rectilinearly movable axle 40 to a position mostlyadjacent the imaging device 20. Then focus the projection lens of theprojection device 10 to thereby form a clear image of the mark point ofthe projection device onto the surface of the measured object 80. Focusthe imaging lens of the image device 20 to thereby form a clear image ofthe object 80 including the imaged mark point on the object.Additionally move the projection device 10 along the secondrectilinearly movable axle 50 to thereby superpose the image of theimaged mark point which is projected onto the object surface upon themark point of the imaging device 20. In this setting, a triangle ΔABC asillustrated in FIG. 5 is formed by connecting the mark point of theprojection device, the mark point of the imaging device, and the imageof the mark point of the projection device on the object surface. Inaddition, the triangle ΔABC is a right angled one, since the firstrectilinearly movable axle 40 crosses the second rectilinearly movableaxle 50, and a line AB which connects the mark point of the projectiondevice to the mark point of the imaging device is aligned with themoving direction of the second rectilinearly movable axle 50. Therefore,the first step includes measuring a length of the right-angled side AB,and an angle θ when the optical axis of the projection device 10intersects the optical axis of the imaging device 20.

Then reset the first and second grating ruler 60 and 70 to a respectivezero reading. Move the object 80 to a position E along the firstrectilinearly movable axle 40, which results in a reading of a moveddistance as R₁ on the first grating ruler 60. Move the projection device10 to a position D along the second rectilinearly movable axle 50, whichresults in a reading of a moved distance as R₂ on the second gratingruler 70. In this setting, a new right angled triangle ΔADE isconstructed from connecting the mark point 15 of the projection device,the mark point 25 of the imaging device, and the reference point E onthe object. If defining a focal length of the movable imaging lens 29 asF₁, an imaged object distance as Z_(C), an imaged image distance asZ_(CF), a focal length of the movable projection lens 15 as F₂, aprojected object distance as L_(P), and a projected image distanceL_(PF), then the following equations can be given:

$\begin{matrix}{{AD} = {{AB} + R_{2}}} & (1) \\{{\frac{1}{Z_{C}} + \frac{1}{Z_{CF}}} = \frac{1}{F_{1}}} & (2) \\{{Z_{C} + Z_{CF}} = \frac{AD}{{tg}\;\vartheta}} & (3) \\{{L_{P} + L_{PF}} = \frac{AD}{\sin\;\vartheta}} & (4) \\{{\frac{1}{L_{P}} + \frac{1}{L_{PF}}} = \frac{1}{F_{2}}} & (5)\end{matrix}$

Therefore, determine values of the respective Z_(C) and Z_(CP) accordingto Equations (2) and (3), and calculate values of the respective L_(P)and L_(PF) according to Equations (4) and (5). Then performautomatically focusing operation for the movable projection lens andimage lens.

The automatically focusing operation includes moving the movableprojection lens 15 of the projection device 10 to a position whichcorrelates to the projected image distance L_(PF). This movement resultsin forming a clear image of grooves of the master grating onto theobject surface after light rays radiated from the light source passthrough the master grating to the object. Then move the imaging lens ofthe imaging device to a position which correlates to the imaged imagedistance Z_(CF). The movement results in forming interference fringes onthe submaster grating 23, which are the moire fringes, in addition to animage of the object surface having the groove image of the mastergrating which is projected onto the object surface.

Then, the moire fringes are recorded by the imaging camera, which arefurther transferred to the image capture board 100 for digitization. Thedigitized images of the moire fringes are further processed in thecomputer 110 so that a first graph of the digitized more fringes can beobtained.

For obtaining additional three graphs of the moire fringes, move themaster grating of the projection device in the direction which isvertical to the optical axis of the projection device according to amoving distance of a respective quarter, half and three-quarter gratingspace. Therefore, a total of four graphs of the moire fringes can beobtained, which are then recorded by the camera. The graphs are furtherinput into the computer 110 through the image capture board 100. Thenapply the phase-shift algorithm to obtain a phase diagram in the phaseranging from 0 to 2π. The algorithm includes the following equations:

$\begin{matrix}{I_{1} = {I_{0} + {A\;{\sin\left( {\varphi + 0} \right)}}}} & (6) \\{I_{2} = {I_{0} + {A\;{\sin\left( {\varphi + {\pi\frac{1}{2}}} \right)}}}} & (7) \\{I_{3} = {I_{0} + {A\;{\sin\left( {\varphi + \pi} \right)}}}} & (8) \\{I_{4} = {I_{0} + {{Asin}\left( {\varphi + \frac{3\;\pi}{2}} \right)}}} & (9) \\{\varphi = {{tg}^{- 1}\frac{I_{4} - I_{2}}{I_{1} - I_{3}}}} & (10)\end{matrix}$where I₀ is an intensity of the background lights, A is a contrast ofthe fringes; and ω is a phase of the measured point.

Then, calculate the phase data of the phase diagram applying theunwrapping algorithm having principles as:φ₂=φ₁−2π if φ₂−φ₁≧π, and φ₂=φ₁+2π if φ₂=φ₁≦−πThis forms a continuously phase distribution.

The next step of the present invention method is to calculate a highdistribution of the object from applying the respective derivedprojected moire heights and the phase equations in accordance with thefollowing parameters which are known: the imaged object distance Z_(C),imaged image distance Z_(CF), projected image distance, projected objectdistance L_(P), intersected angle θ between the optical axe of therespective projection and imaging devices, and the grating spaceP_(P)=P_(C)=P.

In addition, the equations are versatile, which correlates a randomtriangle established from connecting centers of the respective masterand submaster gratings to the image of the master grating which isprojected on the object surface.

As illustrated in FIG. 6, a coordinate system is established on a planedefined by the projection grating, reference plane (where a surfacepoint of the object is positioned) and reference grating (which is thesubmaster grating). In addition to define the projection grating spaceas P_(P) (or the spatial frequency f_(P)) and the reference gratingspace as P_(C) (or the spatial frequency f_(C)), an equation for theprojection grating is:I _(P)=sin(2πf _(P) X _(P))  (11)(assuming an initial phase to be zero, in addition, if non-sinusoidalfunctions are used in the equation of the projection grating, they canbe converted into a combination of series of sinusoidal functionsthrough the Fourier transformation. However, the first term of theFourier series must be obtained so that the phase can be analyzed).

If X is correlated to X_(P) on the reference plane, therefore

$\begin{matrix}{{{tg}\;\alpha} = \frac{X_{P}}{L_{PF}}} & (12) \\{{\frac{X}{\sin\;\alpha} = {\frac{L_{P}}{\sin\left( {\frac{\pi}{2} - \theta + \alpha} \right)} = \frac{L_{P}}{{\cos\;\theta\;\cos\;\alpha} + {\sin\;\theta\;\sin\;\alpha}}}}{{{which}\mspace{14mu}{is}},{{X = \frac{L_{P}}{{\cos\;\theta\;{ctg}\;\alpha} + {\sin\;\theta}}};}}} & (13)\end{matrix}$

Accordingly, Equation 14 can be obtained from Equations (12) and (13):

$\begin{matrix}{X_{P} = \frac{{XL}_{PF}\cos\;\theta}{L_{P} - {X\;\sin\;\theta}}} & (14)\end{matrix}$

From the equations listed above, it is clear that there is a non-linealrelationship between X_(P) and X, which leads to occurrence ofdistortion of the imaged grating which is projected on the referenceplane. Therefore, the imaged grating will not be equal-spaced any more.An equation therefore can be expressed as follows for the imaged gratingon the reference plane:

$\begin{matrix}{I = {I_{P} = {\sin\left( {2\pi\; f_{P}\frac{{XL}_{PF}\cos\;\theta}{L_{P} - {X\;\sin\;\theta}}} \right)}}} & (15)\end{matrix}$

If now considering the imaging system, an image of the projected gratingis formed on the plane where the reference grating is located.

Referring to FIG. 6, it can find that

$\begin{matrix}{\frac{X}{Z_{C}} = \frac{X_{C}}{Z_{CF}}} & (16)\end{matrix}$so that:

$\begin{matrix}{X = {\frac{Z_{C}}{Z_{CF}}{X_{C}.}}} & (17)\end{matrix}$

Combining Equation (17) with Equation (15), an Equation (18) of thelight intensity distribution can be obtained for the projected gratingimage which is formed at the reference grating plane:

$\begin{matrix}{I_{C} = {\sin\left( {2\pi\; f_{P}\frac{X_{C}Z_{C}L_{PF}\cos\;\theta}{{Z_{CF}L_{P}} - {Z_{C}X_{C}\sin\;\theta}}} \right)}} & (18)\end{matrix}$

If an equation for the reference grating is I_(CR)=sin(2πf_(C)X_(C)+Δ)(19), then an Equation (20) for the mixed light intensity of the moirefringes formed by I_(C) and I_(CR) can be expressed as follows:

$\begin{matrix}\begin{matrix}{I_{CCD} = {I_{C} \times I_{CR}}} \\{= {{\sin\left( {2\pi\; f_{P}\frac{X_{C}Z_{C}L_{PF}\cos\;\theta}{{Z_{CF}L_{P}} - {Z_{C}X_{C}\sin\;\theta}}} \right)} \times {\sin\left( {{2\pi\; f_{C}X_{C}} + \Delta} \right)}}} \\{= {\frac{1}{2}\begin{Bmatrix}{{\cos\left\lbrack {{2\pi\; f_{P}\frac{X_{C}Z_{C}L_{PF}\cos\;\theta}{{Z_{CF}L_{P}} - {Z_{C}X_{C}\sin\;\theta}}} - \left( {{2\pi\; f_{C}X_{C}} + \Delta} \right)} \right\rbrack} -} \\{\cos\left\lbrack {{2\pi\; f_{P}\frac{X_{C}Z_{C}L_{PF}\cos\;\theta}{{Z_{CF}L_{P}} - {Z_{C}X_{C}\sin\;\theta}}} + \left( {{2\pi\; f_{C}X_{C}} + \Delta} \right)} \right\rbrack}\end{Bmatrix}}}\end{matrix} & (20)\end{matrix}$

If applying the projected moire fringe interferometry to measure contourof the object surface, it requires that structure of the grating groovescannot be recognized by a CCD camera according to the respective I_(C)and I_(CR). Thus, the second item of Equation (20) is related to effectof high frequencies, which correlates a uniform optical field so that itcannot be recognized by the CCD camera. However, the CCD camera can onlyrecognize optical fields which correlate to moire fringes with lowfrequencies that are described in the first item of Equation (20).Therefore, Equation (20) can be simplified as follows:

$\begin{matrix}{I_{CCD} = {\frac{1}{2}{\cos\left\lbrack {{2\pi\; f_{P}\frac{X_{C}Z_{C}L_{PF}\cos\;\theta}{{Z_{CF}L_{P}} - {Z_{C}X_{C}\sin\;\theta}}} - \left( {{2\pi\; f_{C}X_{C}} + \Delta} \right)} \right\rbrack}}} & (21)\end{matrix}$where f_(P)=f_(C)=f is generally agreed.

If the object is positioned behind the reference plane as illustrated inFIG. 6, and a point of the object which is selected serves as areference point “0” (referring to a zero height of the point), thefollowing Equations (22) and (23) can be obtained:

$\begin{matrix}{\frac{X^{\prime}}{Z_{C}} = {\frac{X - X^{\prime} - {\Delta\; X}}{Z} = {\frac{X - {\Delta\; X}}{Z + Z_{C}} = \frac{X_{Z}}{Z + Z_{C}}}}} & (22) \\{X^{\prime} = {\frac{Z_{C}}{Z + Z_{C}}\left( {X - {\Delta\; X}} \right)}} & (23)\end{matrix}$

Referring to geometrical relationships in the FIG. 6, it shows:

$\begin{matrix}{{\frac{Z}{\Delta\; X} = {{tg}\left( {\frac{\pi}{2} - \theta + \alpha} \right)}},{{{so}\mspace{14mu}{that}\mspace{14mu}\Delta\; X} = {Z{\frac{1 - {{ctg}\;\theta\;{tg}\;\alpha}}{{{ctg}\;\theta} + {{tg}\;\alpha}}.}}}} & (24)\end{matrix}$Equation 24 can be derived as:

$\begin{matrix}{{\Delta\; X} = {Z{\frac{{\sin\;\theta} - {\cos\;\theta\;{tg}\;\alpha}}{{\cos\;\theta} + {\sin\;\theta\;{tg}\;\alpha}}.}}} & (25)\end{matrix}$

In addition, Equation (13) also can be expressed as:

$\begin{matrix}{X = \frac{L_{P}{tg}\;\alpha}{{\cos\;\theta} + {\sin\;\theta\;{tg}\;\alpha}}} & (26)\end{matrix}$

Therefore, a simplified Equation (27) can be obtained by combiningEquations (25), (26) and (12) with Equation (23):

$\begin{matrix}{X_{P} = {L_{PF} \times \frac{{X^{\prime}\left( {Z + Z_{C}} \right)\cos\;\theta} + {{ZZ}_{C}\sin\;\theta}}{{Z_{C}L_{P}} + {{ZZ}_{C}\cos\;\theta} - {{X^{\prime}\left( {Z + Z_{C}} \right)}\sin\;\theta}}}} & (27)\end{matrix}$

Further combining

$X^{\prime} = {\frac{Z_{C}}{Z_{CF}}X_{C}}$with Equation (27), an Equation (28) can be obtained:

$\begin{matrix}{X_{P} = {L_{PF} \times \frac{{Z_{C}{X_{C}\left( {Z + Z_{C}} \right)}\cos\;\theta} + {{ZZ}_{C}Z_{CF}\sin\;\theta}}{{Z_{C}Z_{CF}L_{P}} + {{ZZ}_{C}Z_{CF}\cos\;\theta} - {Z_{C}{X_{C}\left( {Z + Z_{C}} \right)}\sin\;\theta}}}} & (28)\end{matrix}$

Light intensity distribution of projected grating image which is formedon the plane of the reference grating can be described as follows afterit is modulated by the height attitude Z:

$\begin{matrix}\begin{matrix}{I_{C} = {{\sin\left( {2\pi\; f_{P} \times \frac{\begin{matrix}{{Z_{C}{X_{C}\left( {Z + Z_{C}} \right)}\cos\;\theta} +} \\{{ZZ}_{C}Z_{CF}\sin\;\theta}\end{matrix}}{\begin{matrix}{{Z_{C}Z_{CF}L_{P}} + {{ZZ}_{C}Z_{CF}\cos\;\theta} -} \\{Z_{C}{X_{C}\left( {Z + Z_{C}} \right)}\sin\;\theta}\end{matrix}}} \right)} =}} \\{\sin\left( {2\pi\; f_{P} \times L_{PF} \times \frac{{Z\begin{pmatrix}{{Z_{C}Z_{CF}\sin\;\theta} +} \\{Z_{C}X_{C}\cos\;\theta}\end{pmatrix}} + {Z_{C}^{2}X_{C}\cos\;\theta}}{\begin{matrix}{{Z\begin{pmatrix}{{Z_{C}Z_{CF}\cos\;\theta} -} \\{Z_{C}X_{C}\sin\;\theta}\end{pmatrix}} -} \\{{Z_{C}^{2}X_{C}\sin\;\theta} + {Z_{C}Z_{CF}L_{P}}}\end{matrix}}} \right.}\end{matrix} & (29)\end{matrix}$

In addition, the grating equation can be rewritten asI _(CR)=sin(2πf _(C) X _(C)+Δ)  (9)Then, if considering facts of I_(CCD)=I_(C)×I_(CR) and the highfrequency grating structure which cannot be recognized, lead thefollowing Equation (30):

$\begin{matrix}{I_{CCD} = {\frac{1}{2}\cos{\quad{\quad\left\lbrack {{2\pi\; f_{P}L_{PF}\frac{\begin{matrix}{{Z\left( {{Z_{C}Z_{CF}\sin\;\theta} + {Z_{C}X_{C}\cos\;\theta}} \right)} +} \\{Z_{C}^{2}X_{C}\cos\;\theta}\end{matrix}}{\begin{matrix}{{Z\left( {{Z_{C}Z_{CF}\cos\;\theta} - {Z_{C}X_{C}\sin\;\theta}} \right)} -} \\{{Z_{C}^{2}X_{C}\sin\;\theta} + {Z_{C}Z_{CF}L_{P}}}\end{matrix}}} - \left( {{2\pi\; f_{C}X_{C}} + \Delta} \right)} \right\rbrack}}}} & (30)\end{matrix}$Generally, f_(p)=f_(c)=f. If Z=0, Equation (30) can be simplified toEquation (21), which also proves correctness of the above mathematicaldeduction.

In addition, the phase can be expressed as:

$\begin{matrix}{\varphi = {{2\pi\; f_{P}L_{PF}\frac{{ZA} + B}{{ZC} + D}} - \left( {{2\pi\; f_{C}X_{C}} + \Delta} \right)}} & (31)\end{matrix}$

where,A=Z _(C) Z _(CF) sin θ+Z _(C) X _(C) cos θ B=Z _(C) ² X _(C) cos θC=Z _(C) Z _(CF) cos θ−Z _(C) X _(C) sin θ D=− Z _(C) ² X _(C) sin θ+Z_(C) Z _(CF) L _(P)

In terms of Equation (31), calculating the phase of the origin of thecoordinates: X_(C)=0, Y_(C)=0, Z=0, which are combined with Equation(21) to thereby obtain: φ₀=−Δ. Here, φ₀ can be eliminated since it is aconstant which is added to all the phases. This means to treat all thephases as the following operation:φ=φ−φ₀  (31-1);therefore, a full-field phase can be obtained as:

$\begin{matrix}{\varphi = {{2\pi\; f_{P}L_{PF}\frac{{ZA} + B}{{ZC} + D}} - {2\pi\; f_{C}X_{C}}}} & (32)\end{matrix}$

If applying f_(P)=f_(C)=f, Z can be expressed as:

$\begin{matrix}{Z = {- \frac{{\left( {\frac{\varphi}{2\pi\; f} + X_{C}} \right)D} - {L_{PF}B}}{{\left( {\frac{\varphi}{2\pi\; f} + X_{C}} \right)C} - {L_{PF}A}}}} & (33)\end{matrix}$Combining Equations (22) and (17) to thereby obtain Equation (34):

$\begin{matrix}{X_{Z} = {{\frac{Z + Z_{C}}{Z_{C}}X^{\prime}} = {{{\frac{Z + Z_{C}}{Z_{C}} \cdot \frac{Z_{C}}{Z_{CF}}}X_{C}} = {\frac{Z + Z_{C}}{Z_{CF}}X_{C}}}}} & (34)\end{matrix}$

In addition, since Y_(Z) possesses the same proportional relationship asX_(Z), thus

$\begin{matrix}{Y_{Z} = {\frac{Z + Z_{C}}{Z_{CF}}Y_{C}}} & (35)\end{matrix}$

Therefore, a group of completed equations for calculating the respectiveX_(Z), Y_(Z), Z can be finally obtained:

$\begin{matrix}{{Z = {- \frac{{\left( {\frac{\varphi}{2\pi\; f} + X_{C}} \right)D} - {L_{PF}B}}{{\left( {\frac{\varphi}{2\pi\; f} + X_{C}} \right)C} - {L_{PF}A}}}}{X_{Z} = {\frac{Z + Z_{C}}{Z_{CF}}X_{C}}}{Y_{Z} = {\frac{Z + Z_{C}}{Z_{CF}}Y_{C}}}} & (36)\end{matrix}$

Applying the above equations, it is necessary to first operate a heightconversion for solving the height distribution. Then perform a positiontransformation applying the last two equations of the equation group(36) to obtain X_(Z) and Y_(Z). Repeat the above illustrated procedures,an absolute contour of a full fielded 3D surface of the object can beconstructed.

EXAMPLES

The following examples are provided for the purpose of illustration onlyand not limitation.

Example 1

Referring to FIG. 2, there is previously illustrated the imaging device20, which is positioned on the marble table 90. The first rectilinearlymovable axle 40 having a length of 1000 mm with a dust cover is alsoinstalled on the platform to align with the optical axis of the imagingdevice 20. The first axle 40 which is driven by a hand wheel is madefrom THK Cooperation, Japan. The object receiving platform 30 isrotatably in 360 degrees affixed to the movable plate which is slidablyconnected to the axle 40. An object 80, which is a blade of an aviationengine, is positioned on the platform 30. The first grating ruler 60 isinstalled in parallel with the axle 40. The second rectilinearly movableaxle 50 having a length of 400 mm with a dust cover is also installed onthe platform to be perpendicular to the first axle 40. The second axle50 which is also driven by a hand wheel is made from THK Cooperation,Japan. The projection device 10 is affixed to a movable plate which isslidably affixed onto the second rectilinearly movable axle 50, wherethe optical axis of the projection device 10 intersects the second axle50 at angle γ. The second grating ruler 70 is installed in parallel withthe second axle 50.

As further illustrated, the projection device 10 connects to anelectricity source 190 through an electrical wire C07. The measuringcamera 21 and imaging camera 28 of the imaging device 20 through therespective cables C08 and C09 are connected to the Matrox Pulser imagecapture board 100 having four channels, wherein the board 100 isinstalled in the computer 110. All the linear positioners are from PICooperation, Germany, where the positioner 16 is of the model M224.20for the projection lens of the projection device, the positioner 17 isof the model M222.20 for the master grating, and the positioner 29A isof the model M224.20 for the movable imaging lens of the imaging device.They are electrically connected to a direct current motor control board180 (C-842.40) having four channels through the respective electricalcables C01, C02 and C03, wherein the control board is also installed inthe computer 110.

The projection device 10 is illustrated in FIG. 3, comprising the lightsource 11 which is positioned in front of the condenser 12, the mastergrating 13 which is positioned in front of the mark point 14 having thecross shape, and the movable projection lens 15. The master grating 13is movable aligning with an orientation of the grating surface, whichmovement is controlled by the linear positioner 17. The projection lens15 is movable aligning with the optical axis of the projection device,whose movement is controlled by the linear positioner 16.

Referring to FIG. 4, the imaging device includes an alternativeembodiment comprising the measuring light path 120 and imaging lightpath 130.

The imaging light path 130 includes the movable imaging lens 29, thelinear positioner 29A which controls the movement of the movable imaginglens 29, the square prism 24 which is positioned between the image lens29 and submaster grating 23, the mark point 25 which is positionedbetween the square prism 24 and the reflection mirror 26 which reflectsan incident light at 90 degrees, and the imaging camera 28 having acamera lens 27 for recording the imaged mark point 25 having the crossshape.

The measuring optical path 120 includes the movable imaging lens 29, thelinear positioner 29A which controls movement of the movable imaginglens 29 aligning with its optical axis, the submaster grating 23, themeasuring camera 21 having a camera lens 22 for receiving images of themoire fringes positioned on the submaster grating 23.

During the measurement of the object, first adjust the linear positioner16 of the projection device 10 to focus the movable projection lens 15,which forms a clear image of the mark point 14 of the cross on theobject. Then adjust the linear positioned 29A to focus the movableimaging lens 29, which forms a clear image on the imaging camera 28 ofthe imaging device 20, wherein the image is the imaged mark point of thecross 14 positioned on the object. Then through additionally adjustingthe second rectilinearly movable axle 50, make the image of theprojected cross 14 on the object surface superpose upon the image of thecross 25 of the imaging device 20. In this situation, following steps of(2), (3) and (4) which are illustrated in FIG. 7, conduct theautomatically focusing, which is to focus the projection lens throughoperation of the linear positioned 16, so that the grooves of the mastergrating are clearly imaged on the subject surface. Then through a fineoperation of the linear positioner 29A, make the imaging lens 29 whichis finely focused form a clear image on the camera of the imaged grooveswhich are projected on the object surface. Under this condition, conductoperation following steps of (5), (6), (7) and (8) which are illustratedin FIG. 7, wherein the operation includes moving the master grating ofthe projection device in the direction which is vertical to the opticalaxis of the projection device according to a moved distance of arespective quarter, half and three-quarter grating space, so that atotal of four graphs of the moire fringes can be obtained.

Then input the moire fringes recorded on the measuring camera into theimage capture board 100, which results in inputting the digitized moirefringed into the computer 110. Accordingly, diagrams of the digitizedfringes are obtained. Then apply the phase-shift algorithm to calculatea phase diagram ranging from 0 to 2π. Finally, reference the zero phaseof the mark point and the equations, calculate the height distributionof one position of the subject surface, and repeatedly these procedures,obtain X_(Z), Y_(Z) and Z of ever point of the object surface to therebyacquire accurate contour of the full fielded 3D surface of the object.It will be appreciated that an accuracy can be ±0.01 mm applying thepresent invention apparatus and method.

Example 2

Referring to FIG. 2, there is previously illustrated the imaging device20 (see FIG. 9), which is positioned on the marble table 90. The firstrectilinearly movable axle 40 having a length of 1000 mm with a dustcover is also installed on the platform to align with the optical axisof the imaging device 20. The first axle 40 which is driven by a handwheel is made from THK Cooperation, Japan. The object receiving platform30 is rotatably in 360 degrees affixed to the movable plate which isslidably connected to the axle 40. An object 80, which is a blade of anaviation engine, is positioned on the platform 30. The first gratingruler 60 is installed in parallel with the axle 40. The secondrectilinearly movable axle 50 having a length of 400 mm with a dustcover is also installed on the platform to be perpendicular to the firstaxle 40. The second axle 50 which is also driven by a hand wheel is madefrom THK Cooperation, Japan. The projection device 10 is affixed to amovable plate which is slidably affixed onto the second rectilinearlymovable axle 50, where the optical axis of the projection device 10intersects the second axle 50 at angle γ. The second grating ruler 70 isinstalled in parallel with the second axle 50.

As further illustrated, the projection device 10 connects to anelectricity source 190 through the electrical wire C07. The measuringcamera 21 and imaging camera 28 of the imaging device 20 through therespective cables C08 and C09 are connected to the Matrox Pulser imagecapture board 100 having four channels, wherein the board 100 isinstalled in the computer 110. All the linear positioners are from PICooperation, Germany, where the positioner 16 is of the model M224.20for the projection lens of the projection device, the positioner 17 isof the model M222.20 for the master grating, and the positioner 29A isof the model M224.20 for the movable imaging lens of the imaging device.They are electrically connected to a direct current motor control board180 (C-842.400) having four channels from PI Cooperation, Germanythrough the respective electrical cables C01, C02 and C03, wherein thecontrol board is also installed in the computer 110.

The projection device 10 is illustrated in FIG. 8, comprising the lightsource 11, the condenser 12, a round mark point 14, the master grating13 whose movement is controlled by the grating linear positioner 17, aswitcher 18 for switching the mark point and master grating, and themovable projection lens 15 with the linear positioner 16.

The imaging device 20 is illustrated in FIG. 9, comprising the measuringcamera 21 with the camera lens 22, the switcher 27 for the submastergrating 23 and round mark point 25, and the movable imaging lens 29 witha linear positioner 29A.

During the measurement of the object, first switch the round mark point13 into the projecting light path. Then adjust the linear positioner 16of the projection device 10 to focus the movable projection lens 15,which makes a clear image of the round mark point on the object. Thenswitch the round mark point 25 of the imaging device 20 into the imaginglight path. Adjust the linear positioned 29A to focus the movableimaging lens 29 and adjust the length of the second rectilinearlymovable axle 50, which makes an image of the projected round mark point13 on the object surface superpose upon the image of the round markpoint 25 of the imaging device 20 on the measuring camera 21. In thissituation, perform steps of (2), (3) and (4) which are illustrated inFIG. 7, and then conduct automatically focusing, which is, switch themaster grating 13 into the projecting light path, and switch thesubmaster grating 23 into the imaging light path. Under this condition,conduct operation following steps of (5), (6), (7) and (8) which areillustrated in FIG. 7, an accurate contour of the full field 3D surfaceof the object can be obtained with an accuracy of ±0.01 mm. Additionalprocedures can be seen in EXAMPLE 1.

The present invention method and apparatus for measuring contour of the3D object surface applying the moire fringes includes: applying a methodand apparatus of the projected moire interferometry to form graphs ofthe moire fringes containing information related to a heightdistribution of surface points of the measured objects; inputting dataof light intensities of the optical images which are recorded by thecamera into a computer through application of the image capture board;digitizing the graphs of the moire fringes as a pre-data processing ofthe computation; analyzing a plurality of the moire fringe graphsapplying unwrapping algorithm after the graphs have been first treatedby the phase shift algorithm; and obtaining phase diagrams containingdigitized height information of the measured object surface and valuesof the X, Y and Z coordinates of every surface point to thereby completemeasurement of the absolute contour of the 3D surface, which illustratesa dynamic 3D surface of the measured objects and provides data of themeasured surface.

The present invention accomplishes measuring the absolute contour offull fielded 3D surface of objects. The accuracy is ±0.01 mm from thepresent invention, which are 10-15 folds better, as compared with thecurrently available commercial instrument. In addition, the measurementcan be completed with 30 seconds applying the present invention methodand apparatus. Therefore, the method and apparatus which possess a highaccuracy and speed is particularly useful for measuring objects havingsophisticated 3D surface such as the engines.

Of course the present invention is not intended to be restricted to anyparticular form or arrangement, or any specific embodiment, or anyspecific use, disclosed herein, since the same may be modified invarious particulars or relations without departing from the spirit orscope of the claimed invention hereinabove shown and described of whichthe apparatus or method shown is intended only for illustration anddisclosure of an operative embodiment and not to show all of the variousforms or modifications in which this invention might be embodied oroperated.

1. An apparatus for measuring a contour of an object, comprising: a. aprojection device having a projecting optical axis comprised of a lightsource, a movable projection lens, a first grating having a plurality ofgrating grooves and a first mark point; b. an imaging device having animaging optical axis comprised of a movable imaging lens, a secondgrating including multiple grooves, a second mark point and a firstcamera; c. a first rectilinearly movable axle which is positionedperpendicular to a second rectilinearly movable axle, wherein saidobject is rotatably and movably positioned on said first rectilinearlymovable axle which is aligned with said imaging optical axis of saidimaging device, said projection device is movably positioned on saidsecond rectilinearly movable axle; d. means for adjusting positions ofthe respective projection device and object to construct an initialright angled triangle from connecting said first mark point of saidprojection device, said second mark point of said imaging device and animage of said first mark point of said projection device which isprojected onto said object; e. means for further adjusting positions ofthe respective projection device and object to construct a subsequentright angled triangle from connecting said first mark point of saidprojection device, said second mark point of said imaging device and animage of said first mark point of said projection device which isprojected onto said object, means for obtaining data of said subsequentright angled triangle including the projected object and image distancesand the imaged object and imaged distances; f. means for automaticallyrefocusing said projection lens and imaging lens which results inobtaining four sequential graphs of moire fringes; g. means forcalculating a phase diagram according to said graphs containing saidmoire fringes; h. means for calculating phase data of surface points ofsaid object according to a zero phase which is defined for said image ofsaid first mark point which is projected on said object; and i. meansfor calculating altitude distribution of said surface points of saidobject to thereby obtain an absolute full field three dimensionalcontour of said object with a high accuracy.
 2. The apparatus as claimedin claim 1, further comprising first and second grating rulers which arepositioned in parallel with the respective first and secondrectilinearly movable axles.
 3. The apparatus as claimed in claim 1,further comprising a first rotating plate which is movably and rotatablypositioned on said first rectilinearly movable axle, wherein said objectis positioned onto said first rotating plate, and said projectingoptical axis of said projection device intersects said firstrectilinearly movable axle at an angle.
 4. The apparatus as claimed inclaim 1, wherein said first mark point is positioned on one side of saidfirst grating of said projection device as compared with said grooveswhich are positioned on the opposite side of said first grating.
 5. Theapparatus as claimed in claim 1, further comprising that said first markpoint is positioned in parallel with said grooves of said first gratingwhich is positioned in reference to said projecting optical axis.
 6. Theapparatus as claimed in claim 5, further comprising a first switcherwhich can switch the respective grating having said grooves and saidfirst market point alternatively respectively in or off said projectingoptical axis of said projection device.
 7. The apparatus as claimed inclaim 1, further comprising a linear grating positioner in saidprojection device which can sequentially move said first grating alongan orientation of said grating sides according to a predetermineddistance including the respective quarter, a half, and a three quarterof a grating space.
 8. The apparatus as claimed in claim 1, wherein saidsecond mark point is positioned in parallel with said multiple groovesof said second grating which is positioned in reference to saidprojecting optical axis.
 9. The apparatus as claimed in claim 8, furthercomprising a second switcher which can switch said second grating havingsaid multiple grooves and said second mark point alternativelyrespectively in or off said imaging optical axis of said imaging device.10. The apparatus as claimed in claim 1, wherein a type of said firstand second gratings includes a Ronchi grating or sinusoidal grating. 11.The apparatus as claimed in claim 1, wherein said first and second markpoints are in either a cross or a round shape.
 12. The apparatus asclaimed in claim 1, further comprising a first and second linearpositioners for moving the respective projection lens and imaging lensalong the respective optical axe.
 13. The apparatus as claimed in claim1, wherein said imaging device is further comprised of an imaging lightpath and a measuring light path, said measuring light path comprisingsaid movable imaging lens with said second linear positioner, saidsecond grating, and a measuring camera having a camera lens, saidimaging light path comprising said movable imaging lens with said secondlinear positioner, a square prism, said second mark point, a reflectionmirror, an imaging camera having an imaging lens.
 14. The apparatus asclaimed in claim 1, wherein said light source includes a white light.15. The apparatus as claimed in claim 1, further comprising an imagecapture board and a computer which installs said board for imagingprocessing.
 16. An apparatus for measuring a contour of an object,comprising: a. a projection device having a projecting optical axiscomprising a light source, a movable projection lens, a first gratingand a first mark point; b. an imaging device having an imaging opticalaxis comprising a movable imaging lens, a second grating, a second markpoint and a first camera; c. a first rectilinearly movable axle which ispositioned perpendicular to a second rectilinearly movable axle, whereinsaid object is rotatably and movably positioned on said firstrectilinearly movable axle which is aligned with said imaging opticalaxis of said imaging device, said projection device is movablypositioned on said second rectilinearly movable axle wherein theprojecting optical axis intersects said first rectilinearly movable axleat an angle; and d. means for sequentially adjusting positions of therespective projection device and object to construct sequential rightangled triangles from connecting the respective first mark point of saidprojection device, the second mark point of said imaging device and animage of said first mark point of said projection device which isprojected onto said object to thereby obtain sequential graphs of moirefringes for an absolute full fielded three dimensional contour of saidobject with a high accuracy.
 17. A method for measuring a contour of anobject, comprising steps of: a. providing a projection device having aprojecting optical axis comprised of a light source, a movableprojection lens, a first grating having a plurality of grating groovesand a first mark point; b. providing an imaging device having an imagingoptical axis comprised of a movable imaging lens, a second gratingincluding multiple grooves, a second mark point and a first camera; c.providing a first rectilinearly movable axle which is positionedperpendicular to a second rectilinearly movable axle, wherein saidobject is rotatably and movably positioned on said first rectilinearlymovable axle which is aligned with said imaging optical axis of saidimaging device, said projection device is movably positioned on saidsecond rectilinearly movable axle; d. adjusting positions of therespective projection device and object to construct an initial rightangled triangle ABC by connecting said first mark point of saidprojection device, said second mark point of said imaging device and animage of said first mark point of said projection device which isprojected onto said object; e. further adjusting positions of therespective projection device and object to construct a subsequent rightangled triangle ADE by connecting said first mark point of saidprojection device, said second mark point of said imaging device and animage of said first mark point of said projection device which isprojected onto said object, means for obtaining data of said subsequentright angled triangle including projected object and image distances andimaged object and imaged distances; f. automatically refocusing saidprojection lens and imaging lens which results in obtaining foursequential graphs of moire fringes; g. calculating a phase diagramaccording to said graphs containing said moire fringes; h. determiningphase data of surface points of said object according to a zero phasewhich is defined for said image of said first mark point which isprojected on said object; and i. calculating altitude distribution ofsaid surface points of said object to thereby obtain an absolute fullfielded three dimensional contour of said object with a high accuracy.18. The method as claimed in claim 17, wherein constructing said initialright angled triangle ABC is further comprised of steps of: a. movingsaid object along said first rectilinearly movable axle to a position“C” mostly close said imaging device; b. focusing said projection lensto thereby form an image of said first mark point of said projectiondevice on a surface of said object; c. focusing said imaging lens tothereby form an image of said object including said imaged first markpoint on said object; d. moving said projection device along said secondrectilinearly movable axle to thereby superpose said image of saidimaged first mark point upon said second mark point of said imagingdevice; and e. obtaining data of said initial right angled triangle ABCincluding an angle θ which is formed by intersecting said optical axisof said projection device and said optical axis of said imaging device,a length of a line AB which is a distance between said first mark pointat a position B and said second mark point at a position A, and saidlength of said line AB determined from including a reading of a secondgrating ruler which is positioned in parallel with said secondrectilinearly movable axle.
 19. The method as claimed in claim 18,wherein constructing said subsequent right angled triangle is furthercomprised of the steps of: a. moving said projection device with adistance R₂ to a position D along said second rectilinearly movableaxle, wherein a value of R₂ which is equal to a length of a line BD canbe obtained from a reading of said second grating ruler; b. moving saidobject with a distance R₁ to a position E along said first rectilinearlymovable axle, wherein a value of R₁ which equals a length of a line CEcan be obtained by reading a first grating ruler which is positioned inparallel with said first rectilinearly movable axle; and c. determininga projected object distance as L_(P), a project image distance asL_(PF), an imaged object distance as Z_(C), and an imaged image distanceas Z_(CF) applying following Equations [1-5]:AD=AB+R ₂  [1]1/Z _(C)+1/Z _(CF)=1/F ₁  [2]Z _(C) +Z _(CF) =AD/tg θ  [3]L _(P) +L _(PF) =AD/sin θ  [4]1/L _(P)+1/L _(PF)=1/F ₂  [5] wherein θ=arc tg R₂/R₁, F₁ and F₂ arefocal lengths of the respective projection lens and imaging lens. 20.The method as claimed in claim 19, wherein said step of automaticallyrefocusing is further comprised of the steps of: a. moving saidprojection lens along said projecting optical axis to a position whichcorrelates to said project image distance L_(PF); b. moving said imaginglens along said imaging optical axis to a position which correlates tosaid project image distance Z_(CF); c. recording a first graph of moirefringes which are positioned on said second grating of said imagingdevice from applying said imaging camera; and d. moving said firstgrating along an orientation of its grating surface according to amoving distance of a respective quarter, half and three-quarter gratingspace to thereby obtain additional three graphs of moire fringes. 21.The method as claimed in claim 17, wherein said step of calculating aphase diagram is further comprised of applying the following Equations[6-10]:I ₁ =I ₀ +A sin(φ+0)  [6]I ₂ =I ₀ +A sin(φ+π1/2)  [7]I ₃ =I ₀ +A sin(φ+π)  [8]I ₄ =I ₀ +A sin(φ+π3/2)  [9]φ=arc tg(I ⁴⁻ I ₂)/(I ₁ −I ₃)  [10] where φ is a phase of a measuredsurface point of said object, I₀ is an intensity of background lights,and A is a constant of said moire fringes.
 22. The method as claimed inclaim 17, wherein said calculating phase data is further comprised ofapplying the principles of:φ₂=φ₁−2π if φ₂−φ₁≧π, and φ₂=φ₁+2π if φ₂−φ₁≦−π.
 23. The method as claimedin claim 17, wherein said calculating altitude distribution of surfacepoints of said object is further comprised of applying a group ofequations:Z={(φ/2πf+X _(C))D−L _(PF) B}/{(φ/2πf+X _(C))D−L _(PF) A};X _(Z) =X _(C)(Z+Z _(C))/Z _(CF); andY _(Z) =Y _(C)(Z+Z _(C))/Z _(CF) where X_(Z), Y_(Z) and Z are threedimensional coordinates of respective surface points of said object, andfactors of A, B, C and D can be obtained from the respective equations:A=Z _(C) Z _(CF) sin θ+Z _(C) Z _(CF) cos θ;B=Z² _(C)X_(C) cos θ;C=Z _(C) Z _(CF) cos θ−Z _(C) Z _(CF) sin θ; andD=−Z ² _(C) X _(C) sin θ+Z _(C) Z _(CF) L _(P).
 24. A method formeasuring contour of an object, comprising steps of: a. providing aprojection device having a projecting optical axis comprising a lightsource, a movable projection lens, a first grating and a first markpoint; b. providing an imaging device having an imaging optical axiscomprising a movable imaging lens, a second grating, a second mark pointand a first camera; c. providing a first rectilinearly movable axlewhich is positioned perpendicular to a second rectilinearly movableaxle, wherein said object is rotatably and movably positioned on saidfirst rectilinearly movable axle which is aligned with said imagingoptical axis of said imaging device, said projection device is movablypositioned on said second rectilinearly movable axle whose said opticalaxis intersects said first rectilinearly movable axle at an angle; d.sequentially adjusting positions of the respective projection device andobject to construct sequential right angled triangles from connectingthe respective said first mark point of said projection device, saidsecond mark point of said imaging device and an image of said first markpoint of said projection device which is projected onto said object tothereby obtain sequential graphs of moire fringes for an absolute fullfield three dimensional contour of said object with a high accuracy.